A school booster club is selling T-shirts. The silk screening company is selling shirts to the boosters for $3 each, plus a one-time fee of $150 to cover supply costs. If the boosters want to make at least $300 in profits and they sell a shirt for $12, how many shirts do they need to sell?
A.35 or more
B.60 or more
C.25 or more
D.50 or more
12x = 3x+150 + 300
12x - 3x = 450
9x = 450
X = 50 Shirts.
To determine how many shirts the boosters need to sell in order to make at least $300 in profits, we can set up a mathematical equation.
Let's assume the number of shirts the boosters need to sell is 'x'.
The total cost for the shirts will be the cost per shirt multiplied by the number of shirts, which is $3x.
So, the total cost for the shirts, including the one-time fee of $150, will be $3x + $150.
The selling price for each shirt is $12.
The total revenue from selling 'x' shirts will be the selling price per shirt multiplied by the number of shirts, which is $12x.
To calculate the profit, we subtract the total cost from the total revenue:
Profit = Revenue - Cost.
In this case, the profit should be equal to or greater than $300, so we can set up the equation:
$12x - ($3x + $150) ≥ $300.
Simplifying this equation, we have:
$12x - $3x - $150 ≥ $300.
Combine like terms:
$9x - $150 ≥ $300.
Move the constant terms to the right side of the inequality:
$9x ≥ $300 + $150.
$9x ≥ $450.
Divide both sides of the inequality by 9:
x ≥ $450 / $9.
Simplifying further, x ≥ 50.
Therefore, the boosters need to sell at least 50 shirts to make at least $300 in profits.
The correct answer is option D. 50 or more.